Ubuntu tablet applications (including browsers) will basically be adapted versions of the Desktop applications. So, if there is a build of Flash for your processor architecture (I'm not so certain ARM tablets get flash any more, though the Google Chrome Books of course get flash, but using Pepper), you will be able to run flash in your Ubuntu tablet browser.

Flash will not be supported in the Ubuntu Touch web browser by default.

This would require a specific build of flash for the target architecture with hardware acceleration. This is usually provided by OEMs, so unless they have a real interest in supporting flash, I don’t see that happening.

Instead Ubuntu Touch is committed to providing a first-class HTML5 experience. Hopefully modern websites don’t use flash anymore, in favour of open standards.